Mathematics (May 2023)

Convolution, Correlation, and Uncertainty Principles for the Quaternion Offset Linear Canonical Transform

  • Didar Urynbassarova,
  • Aajaz A. Teali

DOI
https://doi.org/10.3390/math11092201
Journal volume & issue
Vol. 11, no. 9
p. 2201

Abstract

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Quaternion Fourier transform (QFT) has gained significant attention in recent years due to its effectiveness in analyzing multi-dimensional signals and images. This article introduces two-dimensional (2D) right-sided quaternion offset linear canonical transform (QOLCT), which is the most general form of QFT with additional free parameters. We explore the properties of 2D right-sided QOLCT, including inversion and Parseval formulas, besides its relationship with other transforms. We also examine the convolution and correlation theorems of 2D right-sided QOLCT, followed by several uncertainty principles. Additionally, we present an illustrative example of the proposed transform, demonstrating its graphical representation of a given signal and its transformed signal. Finally, we demonstrate an application of QOLCT, where it can be utilized to generalize the treatment of swept-frequency filters.

Keywords